4-Stage RC phase shift oscillator

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Safa1902

Joined Nov 19, 2023
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As we know in 3-Stage RC oscillator phase shift the frequency of feedback network is given by f=1/2*pi*R*C*sqrt (2*N) where N is number of stages
in 3-stage the frequency f=1/2*pi*R*C*sqrt (2*3)=1/2*pi*R*C*sqrt (6)
so when i try to get the frequency of 4 stages using same steps (KCL ) I don't get the expected result of f = 1/2*pi*RC*sqrt(8) . anyone can help ??
 

The Electrician

Joined Oct 9, 2007
2,968
View attachment 307943
As we know in 3-Stage RC oscillator phase shift the frequency of feedback network is given by f=1/2*pi*R*C*sqrt (2*N) where N is number of stages
in 3-stage the frequency f=1/2*pi*R*C*sqrt (2*3)=1/2*pi*R*C*sqrt (6)
so when i try to get the frequency of 4 stages using same steps (KCL ) I don't get the expected result of f = 1/2*pi*RC*sqrt(8) . anyone can help ??
You may have found the statement I've shown in red at a web site like this: https://www.electronics-tutorials.ws/oscillator/rc_oscillator.html

That is a mistake; it is only true for N=3. For N=4 or more you will have to work it out for your self, or find the result elsewhere on the web.
 

LvW

Joined Jun 13, 2013
1,749
As we know in 3-Stage RC oscillator phase shift the frequency of feedback network is given by f=1/2*pi*R*C*sqrt (2*N) where N is number of stages
in 3-stage the frequency f=1/2*pi*R*C*sqrt (2*3)=1/2*pi*R*C*sqrt (6)
so when i try to get the frequency of 4 stages using same steps (KCL ) I don't get the expected result of f = 1/2*pi*RC*sqrt(8) . anyone can help ??
No that is not correct.
The expression you have mentioned applies for a three-stage RC oscillator only (leading to SQRT(6) )
More than that, the shown phase values (45 deg) are wrong.

At first, such a network works as a whole only; you cannot divide the total phase shift equally between the individual stages.
In addition, the oscillator frequency results from the condition that the total phase shift must be 180 degrees.
For this reason, at least three RC elements are required to obtain this phase condition at a finite frequency.
 
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